The prediction of crack initiation and propagation in a material using existing finite element computer modeling techniques has been hampered by a number of limitations of the techniques. The existing techniques cannot easily predict the initiation or propagation of cracks in structures containing material or geometric non-linearities or exhibiting non-linear material or geometric response (e.g., as a result of large displacements), cannot easily predict the propagation of multiple crack tips on one-dimensional cracks (either two tips on a single crack, or multiple cracks), and cannot easily handle finite area cracks involving crack fronts.
Two primary approaches have typically been used to predict the initiation and/or the propagation of cracks in layered materials. In one approach, critical energy release rate components govern the growth of the crack. The crack plane is modeled by coincident nodes that are released manually by using the well-known virtual crack closure (VCC) technique [see, for example, Rybicki, E. F. and Kanninen, M. F., “A Finite Element Calculation of Stress Intensity Factors by a Modified Crack Closure Integral”, Engineering Fracture Mechanics, Vol. 9, pp. 931-938 (1977, Pergamon Press)]. The crack tip energy release rate components can be determined from a finite element model with arbitrary non-zero loading on the modeled structure. The crack tip energy release rate components can easily be scaled to the condition where crack propagation will occur if the model is linear. The appropriate nodes along a predetermined crack path can be released and the crack can be propagated for a single one-dimensional crack with a single crack tip. The scaling procedure normally occurs outside the finite element code, after the finite element model has been run on the computer. For a general description of this technique, see Hitchings, D., Robinson, P., and Javidrad, F., “A Finite Element Model for Delamination Propagation in Composites”, Computers & Structures, Vol. 60, No. 6, pp. 1093-1104 (1996, Pergamon Press). In this technique, multiple computer runs are required to propagate the crack, each run corresponding to a different crack length. The technique requires tedious post-processing of multiple finite element solutions. Additionally, if non-linearities exist in the model, difficulties arise in determining the load at which the crack tip energy release rate components would result in crack propagation to occur. Therefore, many experts consider this approach generally applicable only to linear problems. This approach is not practical for addressing problems containing multiple crack tips on one-dimensional cracks, or finite-area cracks.
Traditional interface elements have also been used in finite element models to calculate the propagation of cracks. Such elements invariably require critical release forces, pressures, displacements, or strains to be input to the model, which are then used by the elements to control the release of the interface. To simulate fracture, the critical release forces, pressures, displacements, or strains can be determined using known single mode critical energy release rates, a mixed mode fracture criteria, local finite element model mesh sizes, and stiffnesses. For a general description of traditional interface element approaches, see Wisheart, M. and Richardson, M. O. W., “The Finite Element Analysis of Impact Induced Delamination in Composite Materials Using a Novel Interface Element”, Composites Part A, 29A, pp. 301-313 (1998, Elsevier Science Ltd.); Crisfield, M. A., Mi, Y., Davies, G. A. O., and Hellweg, H-B., “Finite Element Methods and the Progressive Failure-Modelling of Composites Structures”, Computational Plasticity: Fundamentals and Applications '97, CIMNE, Barcelona, Part 1, pp. 239-254 (1997, D. R. J. Owen et al., eds.). Unfortunately, the critical release forces, pressures, displacements, or strains change when the loading is different from that used for calibration, and are dependent on the local mesh size used. This mesh dependence of the release “strength” is particularly troubling for finite-area cracks, as the element aspect ratios may be required to be specific values in the model for the crack to propagate correctly. For these reasons, traditional interface elements have not found widespread use by many technical experts in the fracture mechanics field.